Work, Energy and Power! Work, Energy and Power! The Calculations and Equations

James Joule British physicist James Joule is best known for his work in electricity and thermodynamics Together with the physicist William Thomson (later Baron Kelvin), Joule found that the temperature of a gas falls when it expands without doing any work. This principle, which became known as the Joule-Thomson effect, underlies the operation of common refrigeration and air conditioning systems.British physicist James Joule is best known for his work in electricity and thermodynamics Together with the physicist William Thomson (later Baron Kelvin), Joule found that the temperature of a gas falls when it expands without doing any work. This principle, which became known as the Joule-Thomson effect, underlies the operation of common refrigeration and air conditioning systems. The metric system unit of energy is the joule (J), after James Joule.The metric system unit of energy is the joule (J), after James Joule.

Mechanical Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of positionMechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position Kinetic energy : is the energy of motion Kinetic energy : is the energy of motion Potential Energy : an object can store energy as the result of its position or elastic source Potential Energy : an object can store energy as the result of its position or elastic source

Work Concept Work is defined as a force acting upon an object to cause a displacementWork is defined as a force acting upon an object to cause a displacement Mathematically, work can be expressed by the following equation.Mathematically, work can be expressed by the following equation. W= F x d cos cos 0 0 = 1) W= F x d cos cos 0 0 = 1) where F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vectorwhere F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vector

Work Calculations W=F x dW=F x d cos 30 0 W= F x d =100N X 5m = 100N X 5m X.87 =15Kg(10m/s 2) X 5m =500 N m = 413 N m = 750 N m

Gravitational Potential Energy After an object has been lifted to a height, work is done.After an object has been lifted to a height, work is done. PE = W= F x d= mah PE = W= F x d= mah Potential Energy is maximum at the maximum HEIGHT

Potential Energy Calculation How much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 mHow much potential energy is lost by a 5Kg object to kinetic energy due a decrease in height of 4.5 m PE = mahPE = mah PE = (5Kg)(10 m/s 2 )(4.5 m)PE = (5Kg)(10 m/s 2 )(4.5 m) PE = 225 Kg m 2 /s 2PE = 225 Kg m 2 /s 2 PE = 225 JPE = 225 J

Kinetic Energy Calculation The energy of motionThe energy of motion KE = W= F x d= mah=1/2 mv 2 KE = W= F x d= mah=1/2 mv 2 Find the kinetic energy of an 4 Kg object moving at 5m/s.Find the kinetic energy of an 4 Kg object moving at 5m/s. KE = 1/2 mv 2KE = 1/2 mv 2 KE = ½ (4Kg)(5m/s) 2KE = ½ (4Kg)(5m/s) 2 KE = 50 Kg m 2 /s 2KE = 50 Kg m 2 /s 2 KE = 50 JKE = 50 J

Elastic potential energy

Spring constant Calculation A tired squirrel (mass of 1 kg) does push- ups by applying a force to elevate its center-of-mass by 5 cm. (A) Determine the number of push-ups which a tired squirrel must do in order to do a mere 5.0 Joules of work. (B) Determine the squirrels spring constant.

Spring Constant Calculation W = F x d = 10 N*(.05m)=.5 N mW = F x d = 10 N*(.05m)=.5 N m W =.5 J (each push up) W =.5 J (each push up) 10 pushups = 5 J 10 pushups = 5 J PE = ½ k x 2 PE = ½ k x 2.5 J = ½ k (.05m) 2.5 J = ½ k (.05m) 2.5 J = ½ k (.003m 2 ).5 J = ½ k (.003m 2 ).5 J =.0015 m 2.5 J =.0015 m J/m 2 = k333.3 J/m 2 = k

Power! Power is the rate that we use energy.Power is the rate that we use energy. Power = Work or Energy / TimePower = Work or Energy / Time P = W/t = F x d/t = F vP = W/t = F x d/t = F v The units for power :The units for power : J/sJ/s Kg m 2 / s 2 /sKg m 2 / s 2 /s N m / sN m / s

Power Calculation A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart.A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 seconds. Determine the Power needed to move the cart. P = F x d / tP = F x d / t P = 30 N (10 m) / 5 sP = 30 N (10 m) / 5 s P = 60 N m /sP = 60 N m /s P = 60 wattsP = 60 watts

Summary Energy is the ability to moveEnergy is the ability to move Potential is stored energy (Statics)Potential is stored energy (Statics) Dependant on heightDependant on height Kinetic is moving energy (Dynamics)Kinetic is moving energy (Dynamics) Dependant on velocityDependant on velocity Springs store energy dependant on distance and constantSprings store energy dependant on distance and constant